A study involved a total of 6 barrels of a liquid mixture. If the stan

Standard Deviation : Average Deviation of Terms of a set from the Mean value of the Set

Statement 1: At the start of the study, the researchers were required to remove 30% from each of the volumes of liquid mixture.

Reducing 30% quantity of each barrel will also reduce the deviation of the terms from mean by 30% thereby reducing SD by 30%

SUFFICIENT

Statement 2: The average (arithmetic mean) volume of liquid mixture in the barrels at the end of the study was 63 liters

Average volume of mixture in the barrels doesn't provide any information on how much the difference in the quantities of mixture is in the barrels. Hence,

NOT SUFFICIENT

Answer: option A

Statement 1
We had a total of 6 barrels with some liquid in it. SD at the beginning was 10. If you equally extract 30% from each barrel, the new SD will be 30% lower. Sufficient.

Statement 2
Does not say anything about the new distribution. Hence IS.

This is a GMATPrep question, but they've changed the word "tank" to "barrel" and made some very minor changes to the wording. They haven't even bothered to change the numbers:

during-an-experiment-some-water-was-removed-from-each-of-48424.html

Test takers obviously should not study GMATPrep questions (or near-exact copies) in advance of using the GMATPrep tests, because the GMATPrep tests are the only resource a test taker can trust to give a reliable score estimate. When a test taker knows some of the questions in advance, a test no longer produces a trustworthy score.
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It looks like you're assuming that all the barrels are the same size, Although it doesn't mention that anywhere in the question.

If the barrels are of different sizes then shouldn't the standard deviation change and is not calculable?

1) If we had assume that all barrels had the same amount of mixture then standard deviation would have been zero. Non Zero standard deviation means that all barrels don't have the same amount of Mixture and the the size of Barrels doesn't matter, all that matters is the amount of Mixture in the barrels

2) The standard deviation of a set doesn't change if a constant is added to/subtracted from each terms of the set
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
Reason: The deviation remains same as before if the constant is added to/Subtracted from each term

3) Standard Deviation of the Set changes when a constant term which is not equal to 1 is multiplied with/divides every terms of the set
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
Reason: The deviation gets multiplied by or divided by the same constant that every terms is multiplied or divided with

I hope it helps!

(1) At the start of the study, the researchers were required to remove 30% from each of the volumes of liquid mixture.
So here you are actually multiplying each value in the set with 0.7 hence SD gets multiplied with 0.7
hence suff
(2) The average (arithmetic mean) volume of liquid mixture in the barrels at the end of the study was 63 liters.
Doesnt tell much to know if SD will change or not
Not Suff

Answer A

How can we know that the volume stays constant throughout the study?
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